The foundations of scientific thought are slippery

I was having dinner two friends, a mathematician and a scientist. The mathematician mentioned that “regular” mathematicians (a funny idea) take no notice of the foundations of mathematics. That work belongs to logicians and philosophers. The classic story is about Zermelo-Fraenkel set theory, which is too weak to be really interesting. In other words, it doesn’t assume enough to get to what we consider interesting math. But when you add the special ingredient, the axiom of choice, you get enough power to do interesting math, but you also end up with paradoxes.

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